MinT - Information on Result #947160

Information on Result #947160

Linear OOA(2²¹⁸, 5473, F₂, 3, 30) (dual of [(5473, 3), 16201, 31]-NRT-code), using OOA 3-folding based on linear OA(2²¹⁸, 16419, F₂, 30) (dual of [16419, 16201, 31]-code), using

strength reduction [i] based on linear OA(2²¹⁸, 16419, F₂, 31) (dual of [16419, 16201, 32]-code), using
- constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
  1. linear OA(2²¹¹, 16384, F₂, 31) (dual of [16384, 16173, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  2. linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  3. linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
    - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²²¹, 5474, F₂, 3, 30) (dual of [(5474, 3), 16201, 31]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²¹⁹, 5473, F₂, 3, 30) (dual of [(5473, 3), 16200, 31]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²²⁰, 5473, F₂, 3, 30) (dual of [(5473, 3), 16199, 31]-NRT-code)	[i]	OOA Duplication